Textural information can play an important role in interpretation of a variety of biomedical images, such as X-rays and ultrasound recordings. We have developed a texture segmentation method using texture features extracted by linear filtering. An important component of this system is a new multi-resolution feature reduction module which offers a substantial performance improvement over conventional approaches (principal components or Karhunen-Loeve transform). It is often desirable to reduce the measurement noise that is present in a variety of biomedical images, such as high resolution micrographs, echocardiograms or PET scans. Conventional linear filtering techniques perform well for homogeneous regions but tend to degrade sharp image transitions. In order to preserve the edge information, we have designed an adaptive least squares post-filtering procedure which locally computes a linear combination between the initial noisy image and its filtered version to minimize the estimation error. This method is computationally very efficient and allows an a posterio compensation of some of the deficiencies of conventional noise reduction techniques.